Checking the Adequacy of Fit of Models from Split-Plot Designs

One of the main features that distinguish split-plot experiments from other experiments is that they involve two types of experimental errors: the whole-plot (WP) error and the subplot (SP) error. Taking this into consideration is very important when computing measures of adequacy of fit for split-plot models. In this article, we propose the computation of two R-2, R-2-adjusted, prediction error sums of squares (PRESS), and R-2-prediction statistics to measure the adequacy of fit for the WP and the SP submodels in a split-plot design. This is complemented with the graphical analysis of the two types of errors to check for any violation of the underlying assumptions and the adequacy of fit of split-plot models. Using examples, we show how computing two measures of model adequacy of fit for each split-plot design model is appropriate and useful as they reveal whether the correct WP and SP effects have been included in the model and describe the predictive performance of each group of effects.